void eraApci(double date1, double date2, double ebpv[2][3], double ehp[3], double x, double y, double s, eraASTROM *astrom) /* ** - - - - - - - - ** e r a A p c i ** - - - - - - - - ** ** For a terrestrial observer, prepare star-independent astrometry ** parameters for transformations between ICRS and geocentric CIRS ** coordinates. The Earth ephemeris and CIP/CIO are supplied by the ** caller. ** ** The parameters produced by this function are required in the ** parallax, light deflection, aberration, and bias-precession-nutation ** parts of the astrometric transformation chain. ** ** Given: ** date1 double TDB as a 2-part... ** date2 double ...Julian Date (Note 1) ** ebpv double[2][3] Earth barycentric position/velocity (au, au/day) ** ehp double[3] Earth heliocentric position (au) ** x,y double CIP X,Y (components of unit vector) ** s double the CIO locator s (radians) ** ** Returned: ** astrom eraASTROM* star-independent astrometry parameters: ** pmt double PM time interval (SSB, Julian years) ** eb double[3] SSB to observer (vector, au) ** eh double[3] Sun to observer (unit vector) ** em double distance from Sun to observer (au) ** v double[3] barycentric observer velocity (vector, c) ** bm1 double sqrt(1-|v|^2): reciprocal of Lorenz factor ** bpn double[3][3] bias-precession-nutation matrix ** along double unchanged ** xpl double unchanged ** ypl double unchanged ** sphi double unchanged ** cphi double unchanged ** diurab double unchanged ** eral double unchanged ** refa double unchanged ** refb double unchanged ** ** Notes: ** ** 1) The TDB date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TDB)=2450123.7 could be expressed in any of these ways, among ** others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in cases ** where the loss of several decimal digits of resolution is ** acceptable. The J2000 method is best matched to the way the ** argument is handled internally and will deliver the optimum ** resolution. The MJD method and the date & time methods are both ** good compromises between resolution and convenience. For most ** applications of this function the choice will not be at all ** critical. ** ** TT can be used instead of TDB without any significant impact on ** accuracy. ** ** 2) All the vectors are with respect to BCRS axes. ** ** 3) In cases where the caller does not wish to provide the Earth ** ephemeris and CIP/CIO, the function eraApci13 can be used instead ** of the present function. This computes the required quantities ** using other ERFA functions. ** ** 4) This is one of several functions that inserts into the astrom ** structure star-independent parameters needed for the chain of ** astrometric transformations ICRS <-> GCRS <-> CIRS <-> observed. ** ** The various functions support different classes of observer and ** portions of the transformation chain: ** ** functions observer transformation ** ** eraApcg eraApcg13 geocentric ICRS <-> GCRS ** eraApci eraApci13 terrestrial ICRS <-> CIRS ** eraApco eraApco13 terrestrial ICRS <-> observed ** eraApcs eraApcs13 space ICRS <-> GCRS ** eraAper eraAper13 terrestrial update Earth rotation ** eraApio eraApio13 terrestrial CIRS <-> observed ** ** Those with names ending in "13" use contemporary ERFA models to ** compute the various ephemerides. The others accept ephemerides ** supplied by the caller. ** ** The transformation from ICRS to GCRS covers space motion, ** parallax, light deflection, and aberration. From GCRS to CIRS ** comprises frame bias and precession-nutation. From CIRS to ** observed takes account of Earth rotation, polar motion, diurnal ** aberration and parallax (unless subsumed into the ICRS <-> GCRS ** transformation), and atmospheric refraction. ** ** 5) The context structure astrom produced by this function is used by ** eraAtciq* and eraAticq*. ** ** Called: ** eraApcg astrometry parameters, ICRS-GCRS, geocenter ** eraC2ixys celestial-to-intermediate matrix, given X,Y and s ** ** Copyright (C) 2013-2016, NumFOCUS Foundation. ** Derived, with permission, from the SOFA library. See notes at end of file. */ { /* Star-independent astrometry parameters for geocenter. */ eraApcg(date1, date2, ebpv, ehp, astrom); /* CIO based BPN matrix. */ eraC2ixys(x, y, s, astrom->bpn); /* Finished. */ }
void eraApco(double date1, double date2, double ebpv[2][3], double ehp[3], double x, double y, double s, double theta, double elong, double phi, double hm, double xp, double yp, double sp, double refa, double refb, eraASTROM *astrom) /* ** - - - - - - - - ** e r a A p c o ** - - - - - - - - ** ** For a terrestrial observer, prepare star-independent astrometry ** parameters for transformations between ICRS and observed ** coordinates. The caller supplies the Earth ephemeris, the Earth ** rotation information and the refraction constants as well as the ** site coordinates. ** ** Given: ** date1 double TDB as a 2-part... ** date2 double ...Julian Date (Note 1) ** ebpv double[2][3] Earth barycentric PV (au, au/day, Note 2) ** ehp double[3] Earth heliocentric P (au, Note 2) ** x,y double CIP X,Y (components of unit vector) ** s double the CIO locator s (radians) ** theta double Earth rotation angle (radians) ** elong double longitude (radians, east +ve, Note 3) ** phi double latitude (geodetic, radians, Note 3) ** hm double height above ellipsoid (m, geodetic, Note 3) ** xp,yp double polar motion coordinates (radians, Note 4) ** sp double the TIO locator s' (radians, Note 4) ** refa double refraction constant A (radians, Note 5) ** refb double refraction constant B (radians, Note 5) ** ** Returned: ** astrom eraASTROM* star-independent astrometry parameters: ** pmt double PM time interval (SSB, Julian years) ** eb double[3] SSB to observer (vector, au) ** eh double[3] Sun to observer (unit vector) ** em double distance from Sun to observer (au) ** v double[3] barycentric observer velocity (vector, c) ** bm1 double sqrt(1-|v|^2): reciprocal of Lorenz factor ** bpn double[3][3] bias-precession-nutation matrix ** along double longitude + s' (radians) ** xpl double polar motion xp wrt local meridian (radians) ** ypl double polar motion yp wrt local meridian (radians) ** sphi double sine of geodetic latitude ** cphi double cosine of geodetic latitude ** diurab double magnitude of diurnal aberration vector ** eral double "local" Earth rotation angle (radians) ** refa double refraction constant A (radians) ** refb double refraction constant B (radians) ** ** Notes: ** ** 1) The TDB date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TDB)=2450123.7 could be expressed in any of these ways, among ** others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in cases ** where the loss of several decimal digits of resolution is ** acceptable. The J2000 method is best matched to the way the ** argument is handled internally and will deliver the optimum ** resolution. The MJD method and the date & time methods are both ** good compromises between resolution and convenience. For most ** applications of this function the choice will not be at all ** critical. ** ** TT can be used instead of TDB without any significant impact on ** accuracy. ** ** 2) The vectors eb, eh, and all the astrom vectors, are with respect ** to BCRS axes. ** ** 3) The geographical coordinates are with respect to the ERFA_WGS84 ** reference ellipsoid. TAKE CARE WITH THE LONGITUDE SIGN ** CONVENTION: the longitude required by the present function is ** right-handed, i.e. east-positive, in accordance with geographical ** convention. ** ** 4) xp and yp are the coordinates (in radians) of the Celestial ** Intermediate Pole with respect to the International Terrestrial ** Reference System (see IERS Conventions), measured along the ** meridians 0 and 90 deg west respectively. sp is the TIO locator ** s', in radians, which positions the Terrestrial Intermediate ** Origin on the equator. For many applications, xp, yp and ** (especially) sp can be set to zero. ** ** Internally, the polar motion is stored in a form rotated onto the ** local meridian. ** ** 5) The refraction constants refa and refb are for use in a ** dZ = A*tan(Z)+B*tan^3(Z) model, where Z is the observed ** (i.e. refracted) zenith distance and dZ is the amount of ** refraction. ** ** 6) It is advisable to take great care with units, as even unlikely ** values of the input parameters are accepted and processed in ** accordance with the models used. ** ** 7) In cases where the caller does not wish to provide the Earth ** Ephemeris, the Earth rotation information and refraction ** constants, the function eraApco13 can be used instead of the ** present function. This starts from UTC and weather readings etc. ** and computes suitable values using other ERFA functions. ** ** 8) This is one of several functions that inserts into the astrom ** structure star-independent parameters needed for the chain of ** astrometric transformations ICRS <-> GCRS <-> CIRS <-> observed. ** ** The various functions support different classes of observer and ** portions of the transformation chain: ** ** functions observer transformation ** ** eraApcg eraApcg13 geocentric ICRS <-> GCRS ** eraApci eraApci13 terrestrial ICRS <-> CIRS ** eraApco eraApco13 terrestrial ICRS <-> observed ** eraApcs eraApcs13 space ICRS <-> GCRS ** eraAper eraAper13 terrestrial update Earth rotation ** eraApio eraApio13 terrestrial CIRS <-> observed ** ** Those with names ending in "13" use contemporary ERFA models to ** compute the various ephemerides. The others accept ephemerides ** supplied by the caller. ** ** The transformation from ICRS to GCRS covers space motion, ** parallax, light deflection, and aberration. From GCRS to CIRS ** comprises frame bias and precession-nutation. From CIRS to ** observed takes account of Earth rotation, polar motion, diurnal ** aberration and parallax (unless subsumed into the ICRS <-> GCRS ** transformation), and atmospheric refraction. ** ** 9) The context structure astrom produced by this function is used by ** eraAtioq, eraAtoiq, eraAtciq* and eraAticq*. ** ** Called: ** eraAper astrometry parameters: update ERA ** eraC2ixys celestial-to-intermediate matrix, given X,Y and s ** eraPvtob position/velocity of terrestrial station ** eraTrxpv product of transpose of r-matrix and pv-vector ** eraApcs astrometry parameters, ICRS-GCRS, space observer ** eraCr copy r-matrix ** ** Copyright (C) 2013-2016, NumFOCUS Foundation. ** Derived, with permission, from the SOFA library. See notes at end of file. */ { double sl, cl, r[3][3], pvc[2][3], pv[2][3]; /* Longitude with adjustment for TIO locator s'. */ astrom->along = elong + sp; /* Polar motion, rotated onto the local meridian. */ sl = sin(astrom->along); cl = cos(astrom->along); astrom->xpl = xp*cl - yp*sl; astrom->ypl = xp*sl + yp*cl; /* Functions of latitude. */ astrom->sphi = sin(phi); astrom->cphi = cos(phi); /* Refraction constants. */ astrom->refa = refa; astrom->refb = refb; /* Local Earth rotation angle. */ eraAper(theta, astrom); /* Disable the (redundant) diurnal aberration step. */ astrom->diurab = 0.0; /* CIO based BPN matrix. */ eraC2ixys(x, y, s, r); /* Observer's geocentric position and velocity (m, m/s, CIRS). */ eraPvtob(elong, phi, hm, xp, yp, sp, theta, pvc); /* Rotate into GCRS. */ eraTrxpv(r, pvc, pv); /* ICRS <-> GCRS parameters. */ eraApcs(date1, date2, pv, ebpv, ehp, astrom); /* Store the CIO based BPN matrix. */ eraCr(r, astrom->bpn ); /* Finished. */ }
void eraC2i06a(double date1, double date2, double rc2i[3][3]) /* ** - - - - - - - - - - ** e r a C 2 i 0 6 a ** - - - - - - - - - - ** ** Form the celestial-to-intermediate matrix for a given date using the ** IAU 2006 precession and IAU 2000A nutation models. ** ** Given: ** date1,date2 double TT as a 2-part Julian Date (Note 1) ** ** Returned: ** rc2i double[3][3] celestial-to-intermediate matrix (Note 2) ** ** Notes: ** ** 1) The TT date date1+date2 is a Julian Date, apportioned in any ** convenient way between the two arguments. For example, ** JD(TT)=2450123.7 could be expressed in any of these ways, ** among others: ** ** date1 date2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in ** cases where the loss of several decimal digits of resolution ** is acceptable. The J2000 method is best matched to the way ** the argument is handled internally and will deliver the ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** ** 2) The matrix rc2i is the first stage in the transformation from ** celestial to terrestrial coordinates: ** ** [TRS] = RPOM * R_3(ERA) * rc2i * [CRS] ** ** = RC2T * [CRS] ** ** where [CRS] is a vector in the Geocentric Celestial Reference ** System and [TRS] is a vector in the International Terrestrial ** Reference System (see IERS Conventions 2003), ERA is the Earth ** Rotation Angle and RPOM is the polar motion matrix. ** ** Called: ** eraPnm06a classical NPB matrix, IAU 2006/2000A ** eraBpn2xy extract CIP X,Y coordinates from NPB matrix ** eraS06 the CIO locator s, given X,Y, IAU 2006 ** eraC2ixys celestial-to-intermediate matrix, given X,Y and s ** ** References: ** ** McCarthy, D. D., Petit, G. (eds.), 2004, IERS Conventions (2003), ** IERS Technical Note No. 32, BKG ** ** Copyright (C) 2013-2015, NumFOCUS Foundation. ** Derived, with permission, from the SOFA library. See notes at end of file. */ { double rbpn[3][3], x, y, s; /* Obtain the celestial-to-true matrix (IAU 2006/2000A). */ eraPnm06a(date1, date2, rbpn); /* Extract the X,Y coordinates. */ eraBpn2xy(rbpn, &x, &y); /* Obtain the CIO locator. */ s = eraS06(date1, date2, x, y); /* Form the celestial-to-intermediate matrix. */ eraC2ixys(x, y, s, rc2i); return; }